Tortuosity and objective relative acceleration in the theory of porous materials
- Wilmanski, Krzysztof
2010 Mathematics Subject Classification
- 80A17 74A20 74F10 74J10
- Thermodynamics, Biot's model, poroelastic materials, acoustic waves
The aim of this work is twofold. We show the construction of an objective relative acceleration for a two-component mixture and prove that its incorporation in the momentum source requires additional terms in partial stresses and in the energy. This may be interpreted as an influence of tortuosity in the theory of saturated poroelastic materials and a connection of tortuosity with fluctuations of the kinetic energy on a mesoscopic level of observation. The linearization of such a model yields Biot's equations used in poroacoustics. We demonstrate as well that results for the propagation of acoustic waves in saturated poroelastic media are qualitatively similar for Biot's model and for the simple mixture model in which both the tortuosity and the Biot's coupling between partial stresses are neglected. It is also indicated that the coupling constant of Biot's model obtained by means of the Gassmann relation may be too large as it leads to very small differences in the speed of propagation of the P1-wave for small and large frequencies which contradicts the data for soils.
- Proc. Roy. Soc. London Ser. A 461 (2005), pp. 1533--1561.